Diagonalizably linearized coherent sheaves

Coherent Sheaves and Cohesive Sheaves

We consider coherent and cohesive sheaves of O–modules over open sets Ω ⊂ Cn. We prove that coherent sheaves, and certain other sheaves derived from them, are cohesive; and conversely, certain sheaves derived from cohesive sheaves are coherent. An important tool in all this, also proved here, is that the sheaf of Banach space valued holomorphic germs is flat. To Linda Rothschild on her birthday

Coherent Sheaves and Categorical

We introduce the concept of a geometric categorical sl2 action and relate it to that of a strong categorical sl2 action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl2 action induces a strong categorical sl2 action. This allows one to apply the theory of strong sl2 actions to various geometric situations. Our main e...

Linear Koszul duality, II: coherent sheaves on perfect sheaves

In this paper we continue the study (initiated in [MR1]) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change.

Hyperholomorpic connections on coherent sheaves and stability

Abstract Let M be a hyperkähler manifold, and F a torsion-free and reflexive coherent sheaf on M . Assume that F (outside of singularities) admits a connection ∇ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [V2]. Such sheaves are stable ...

Model-theoretic Imaginaries and Coherent Sheaves